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Modeling Microalgal Abundance with Artificial Neural Networks: Demonstration of a Heuristic 'Grey-Box' to Deconvolve And View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by DigitalCommons@University of Nebraska University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Publications, Agencies and Staff of the .SU . U.S. Department of Commerce Department of Commerce 2012 Modeling Microalgal Abundance with Artificial Neural Networks: Demonstration of a Heuristic ‘Grey-Box’ to Deconvolve and Quantify Environmental Influences David F. Millie Palm Island Enviro-Informatics LLC., [email protected] Gary R. Weckman Ohio University - Main Campus William A. Young II Ohio University - Main Campus James E. Ivey Florida Fish and Wildlife Conservation Commission Hunter J. Carrick Central Michigan University See next page for additional authors Follow this and additional works at: http://digitalcommons.unl.edu/usdeptcommercepub Millie, David F.; Weckman, Gary R.; Young, William A. II; Ivey, James E.; Carrick, Hunter J.; and Fahnenstiel, Gary L., "Modeling Microalgal Abundance with Artificial Neural Networks: Demonstration of a Heuristic ‘Grey-Box’ to Deconvolve and Quantify Environmental Influences" (2012). Publications, Agencies and Staff of ht e U.S. Department of Commerce. 501. http://digitalcommons.unl.edu/usdeptcommercepub/501 This Article is brought to you for free and open access by the U.S. Department of Commerce at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Publications, Agencies and Staff of the .SU . Department of Commerce by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Authors David F. Millie, Gary R. Weckman, William A. Young II, James E. Ivey, Hunter J. Carrick, and Gary L. Fahnenstiel This article is available at DigitalCommons@University of Nebraska - Lincoln: http://digitalcommons.unl.edu/usdeptcommercepub/ 501 Environmental Modelling & Software 38 (2012) 27e39 Contents lists available at SciVerse ScienceDirect Environmental Modelling & Software journal homepage: www.elsevier.com/locate/envsoft Modeling microalgal abundance with artificial neural networks: Demonstration of a heuristic ‘Grey-Box’ to deconvolve and quantify environmental influences David F. Millie a,b,c,*, Gary R. Weckman d, William A. Young II e, James E. Ivey c, Hunter J. Carrick f, Gary L. Fahnenstiel g a Palm Island Enviro-Informatics LLC., Sarasota, FL 34232, USA b Loyola University New Orleans, Department of Biological Sciences, New Orleans, LA 70118, USA c Florida Fish & Wildlife Conservation Commission, Fish & Wildlife Research Institute, St. Petersburg, FL 33701, USA d Ohio University, Russ College of Engineering and Technology, Department of Industrial and Systems Engineering, Athens, OH 45701, USA e Ohio University, College of Business, Management Systems Department, Athens, OH 45701, USA f Central Michigan University, Institute for Great Lakes Research, Mount Pleasant, MI 48559, USA g National Oceanic and Atmospheric Administration, Great Lakes Environmental Research Laboratory, Lake Michigan Field Station, Muskegon, MI 49441, USA article info abstract Article history: An artificial neural network (ANN)-based technology e a ‘Grey-Box’, originating the iterative selection, Received 4 February 2012 depiction, and quantitation of environmental relationships for modeling microalgal abundance, as Accepted 10 April 2012 chlorophyll (CHL) a, was developed and evaluated. Due to their robust capability for reproducing the Available online 2 June 2012 complexities underlying chaotic, non-linear systems, ANNs have become popular for the modeling of ecosystem structure and function. However, ANNs exhibit a holistic deficiency in declarative knowledge Keywords: structure (i.e. a ‘black-box’). The architecture of the Grey-Box provided the benefit of the ANN modeling Artificial intelligence structure, while deconvolving the interaction of prediction potentials among environmental variables Ecological modeling fl Environmental informatics upon CHL a. The in uences of (pairs of) predictors upon the variance and magnitude of CHL a were Output response surfaces depicted via pedagogical knowledge extraction (multi-dimensional response surfaces). This afforded Pedagogical knowledge extraction derivation of mathematical equations for iterative predictive outcomes of CHL a and together with an algorithmic expression across iterations, corrected for the lack of declarative knowledge within conventional ANNs. Importantly, the Grey-Box ‘bridged the gap’ between ‘white-box’ parametric models and black-box ANNs in terms of performance and mathematical transparency. Grey-Box formulations are relevant to ecological niche modeling, identification of biotic response(s) to stress/disturbance thresh- olds, and qualitative/quantitative derivation of biota-environmental relationships for incorporation within stand-alone mechanistic models projecting ecological structure. Ó 2012 Elsevier Ltd. All rights reserved. “Ecologists . should be aware that neural networks are not just 1. Introduction black boxes: they can open the hood, see what is in and try some trick.” Scardi (2001) Artificial Neural Networks (ANNs) have become popular tools for modeling phytoplankton abundances and production/toxicity dynamics as a function of environmental ‘predictors’ across diverse aquatic systems (e.g. Recknagel et al., 1997; Barciela et al., 1999; Scardi and Harding,1999; Olden, 2000; Scardi, 2001; Lee et al., 2003; Millie et al., 2006a, 2006b; Teles et al., 2006; Chan et al., 2007; Jeong fi Abbreviations: AMB, ambient temperature; ANN, arti cial neural network; BP, et al., 2008). Briefly, ANNs are a core form of Artificial Intelligence barometric pressure; CHL, chlorophyll; CURDIR, current direction; CURSPD, current models that discern complex associations among variables through speed; DO, dissolved oxygen; MLR, multiple linear regression; NOXÀN, nitrite/ nitrateenitrogen; PAR, photosynthetic active radiation; PE, processing elements; iterative and repetitive data presentation. In essence, the correlated pH, water acidity, basicity; PRECIP, precipitation; RH, relative humidity; SAL, nonlinear patterns between ‘predictor’ and ‘response’ variables are salinity; TEMP, water temperature; TURB, turbidity; URÀN, ureaenitrogen; identified, with the complex interactions reproduced and mapped. WNDDIR, wind direction; WNDSPD, wind speed. Network computations easily accommodate data of non-normal * Corresponding author. Palm Island Enviro-Informatics LLC., 4645 Stone Ridge fl Trail, Sarasota, FL 34232, USA. Tel.: þ1 941 544 7926; fax: þ1 941 378 5769. probability distributions and/or variables re ecting cyclic variation E-mail addresses: [email protected], [email protected] (D.F. Millie). (Maier et al., 1998), traits typically observed within large ‘noisy’, 1364-8152/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.envsoft.2012.04.009 28 D.F. Millie et al. / Environmental Modelling & Software 38 (2012) 27e39 even chaotic environmental data sets (see Peck et al., 2003; Rohani concerning the fundamental relationships of and/or interactive et al., 2004; Murray and Conner, 2009; Wood, 2010). complexities between/among the biotic (response) and environ- ANNs typically have high-dimensional input space and do not mental (predictor) variables, MLR may result in model estimations exhibit any explicit or declarative knowledge structure. Generally, having little or no interpretive relevance (after Millie et al., 2006a). only the input-output characteristics of ANNs are of interest, with Accurate, reproducible prediction of system-level patterns and the ‘knowledge’ of variable relationships encoded almost incom- processes is a basic tenet of ecological forecasting. In order to prehensibly by synaptic weights embedded within network provide worthwhile bases for natural resource stewardship and/or architecture (Fig. 1). Because of this holistic lack of model trans- proactive mitigation of environmental disturbance/stressors, parency, many researchers consider ANNs to be ‘black-boxes’ (Lek statistical-based modeling efforts require a coupling of reliable and Guegan, 1999; Olden and Jackson, 2002) and entrust a low prediction with a conceptual interpretation of biotic structure and confidence to their utilization as empirical models of ecological function (after Millie et al., 2006a,b, 2011). Clearly, a heuristic processes. From this, ANNs might appear to be of limited value for knowledge-extraction technique that provides exact quantitative scientific theory generation, environmental problem solving and/or formulations pertaining to non-linear variable interaction and natural resource decision-making. prediction influences is highly desirable (c.f. Saito and Nakano, Aquatic scientists traditionally have relied upon multivariate 2002). Such an approach would allow for a mathematically linear regression (MLR) to model microalgal-environmental rela- comprehensive, yet pragmatic understanding of environmental- tionships and functionality (e.g. Cattaneo, 1987; Sarnelle, 1992; biota complexity and interaction, whilst (potentially) eliminating Bachmann et al., 1996, 2001; Dodds et al., 2002, 2006; Heffernan the black-box mentality for ANNs. et al., 2010). Such ‘white-box’ parametric models are far less The chlorophyll (CHL) a concentration of a water column is abstract than ANNs - the derivation of defined coefficients (based a universally accepted measurement of planktonic algal abundance on correspondence between the response and predictor variables) and used to quantify community dynamics
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